Question

Density of wood is $0.5\text{g/cc}$ in the $CGS$ system of units. The numerical value of density in $MKS$ system of units is

• A. $500$
• B. $600$
• C. $700$
• D. $800$

Answer 1

The correct option is A $500$

For any physical quantity,
Numerical value $\times$ Unit $=$ constant
$\Rightarrow n_2{u}_2=n_1{u}_1$
$\Rightarrow n_2\left[M_2{L}_2^{-3}{T}_2^0\right]=n_1\left[M_1{L}_1^{-3}{T}_1^0\right]$
$\Rightarrow n_2=n_1\left(\frac{M_1}{M_2}\right){\left(\frac{L_1}{L_2}\right)}^{-3}{\left(\frac{T_1}{T_2}\right)}^0$
$\Rightarrow n_2=0.5\left(\frac{\text{g}}{\text{kg}}\right){\left(\frac{\text{cm}}{\text{m}}\right)}^{-3}{\left(\frac{\text{s}}{\text{s}}\right)}^0$
$\Rightarrow n_2=0.5\times \left(\frac{1}{{10}^3}\right)\times {\left(\frac{1}{100}\right)}^{-3}\times {\left(\frac{1}{1}\right)}^0$
$\Rightarrow n_2=500$